Sets Questions

We provide sets practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on sets skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

List of sets Questions

Question No Questions Class
1 Let ( boldsymbol{O}= ) Set of odd natural numbers ( = )
( {1,3,5,7,9, dots} ) and ( E=operatorname{set} ) of even
natural numbers ( ={2,4,6,8,10, dots dots .} )
Then show that ( 3 in E )
11
2 Draw Venn diagrams to illustrate ( boldsymbol{A} cup )
( (boldsymbol{B} cap boldsymbol{C}) )
11
3 The set of fractions between the natural
numbers 3 and 4 is a :
A. Finite set
B. Null set
c. Infinite set
D. singleton set
11
4 Suppose ( A_{1}, A_{2}, dots, A_{30} ) are thirty sets each having 5 elements and
( B_{1}, B_{2}, dots, B_{n} ) are n sets each with 3 elements. Let ( bigcup_{i=1}^{30} A_{i}=bigcup_{j=1}^{n} B_{j}=S ) and
each elements of ( S ) belongs to exactly 10
of the ( A_{i} ) and exactly 9 of the ( B_{j} . ) Then ( n )
is equal to-
A . 35
B. 45 5
( c .55 )
D. 65
11
5 Find total number of subsets of ( mathrm{B}={mathrm{a} )
( mathbf{b}, mathbf{c}} )
11
6 Given ( boldsymbol{A}=mathbf{2}, mathbf{3}, boldsymbol{B}=mathbf{4}, mathbf{5}, boldsymbol{C}=mathbf{5}, mathbf{6}, ) find
(i) ( boldsymbol{A} times(boldsymbol{B} cap boldsymbol{C})=ldots ldots )
(ii) ( (boldsymbol{A} times boldsymbol{B}) cup(boldsymbol{B} times boldsymbol{C})=ldots ldots )
11
7 ( mathrm{U}={1,2,3,4,5,6,7,8,9,10} )
( mathrm{A}={2,4,6,8,10}, B={1,3,5,7,8,10} )
Find ( (A cup B) )
11
8 If ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{3}, boldsymbol{4}} ) and ( boldsymbol{C}= )
( {1,3,5}, ) then ( A times(B-C)= )
A ( cdot(A times B)-(A times C) )
в. ( (A times B)+(A times C) )
c. ( (A times B)-(B times C) )
D. ( (A times B)-(C times A) )
11
9 Identify the type of set ( boldsymbol{B}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{x}=boldsymbol{2} boldsymbol{n}} )
A. Finite Set
B. Null Set
c. Infinite Set
D. singleton set
11
10 For any two sets ( A ) and ( B ), show that the
following statements are equivalent.
(i) ( boldsymbol{A} subset boldsymbol{B} )
(ii) ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi} )
(iii) ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{B} )
(iv) ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} )
11
11 Write down all possible subsets of the following set. {1,{1}} 11
12 ( a epsilon{a, b, c}, ) then ( {a} ) is a subset of
( {a, b, c} .(text { Enter } 1 text { if true or } 0 text { otherwise }) )
11
13 Which one of the following is not true?
( mathbf{A} cdot A backslash B=A cap B^{prime} )
в. ( A backslash B=A cap B )
C ( . A backslash B=(A cup B) cap B^{prime} )
D. ( A backslash B=(A cup B) backslash B )
11
14 If ( A={1,2,3,4,5,6,7,8} ) and ( B={1,3,5 )
73, then find ( A-B ) and ( A cap B )
( A cdot{3,5} ) and {2,4,6}
B. {2,4,6) and (1,5}
c. {2,4,6,7} and (1,3,5,6)
D. {2,4,6,8} and {1,3,5,7}
11
15 Draw a Venn diagram, showing sub-set relations of the following sets. ( boldsymbol{A}={mathbf{2}, boldsymbol{4}} quad boldsymbol{B}=left{boldsymbol{x} mid boldsymbol{x}=boldsymbol{2}^{n}, boldsymbol{n} leqright. )
( mathbf{5}, boldsymbol{n} in boldsymbol{N}} )
( C={x mid x text { is an even natural number } leq )
( mathbf{1 6}} )
11
16 Place the elements of the following sets
in the proper location on the given Venn
diagram.
( boldsymbol{U}={mathbf{5}, mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}, mathbf{1 0}, mathbf{1 1}, mathbf{1 2}, mathbf{1 3}} )
( M={5,8,10,11}, N={5,6,7,9,10} )
11
17 Let ( boldsymbol{A}={1,2,3,4,5,6,7,8,9,10} . ) Then
the number of subsets of ( A ) containing exactly two elements is
A . 20
B. 40
c. 45
D. 90
11
18 Number of ( P_{2} ) and ( P_{3} ) viewers. 11
19 If ( A={a, b, c, d, e}, B={a, c, e, g} ) and ( C= )
( {b, d, e, g} ) then which of the following is
true?
A ( cdot C subset(A cup B) )
B . ( C subset(A cap B) )
c. ( A cup B=A cup C )
D. Both(1) and (3)
11
20 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{B}-boldsymbol{D} )
11
21 Given, ( boldsymbol{A}={text { Triangles }}, boldsymbol{B}={ )
Isosceles triangles ( } ) ( C={text { Equilateral triangles }} . ) State
whether the following statement are correct or incorrect. Give reasons.
( boldsymbol{C} subset boldsymbol{A} )
11
22 If ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1} boldsymbol{0}) ) and
( boldsymbol{C}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq mathbf{7}} ; ) find :
( boldsymbol{n}(boldsymbol{B}-(boldsymbol{A}-boldsymbol{C})) )
11
23 If ( boldsymbol{P}={text { factors of } 36} ) and ( boldsymbol{Q}={ ) factors of ( 48}, ) find ( Q-P ) 11
24 Use the given figure to find:
Given, ( n(xi)=52, n(A)=43 ) and
( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} )
( boldsymbol{n}(boldsymbol{A}-boldsymbol{B}) )
11
25 Find the intersection of ( A ) and ( B, ) by
representing using Venn diagram:
( boldsymbol{A}={mathbf{1}, mathbf{3}, mathbf{5}, mathbf{7}}, boldsymbol{B}={mathbf{2}, mathbf{5}, mathbf{7}, mathbf{1 0}, mathbf{1 2}} )
( mathbf{A} cdot{1,3,5,7} )
B ( cdot{5,7} )
( mathbf{c} cdot{1,2,3,5,7,10} )
D. None of these
11
26 State whether given set is empty or
not?
Set of even prime numbers
11
27 Write down all possible subsets of the following set. ( {a, b, c} ) 11
28 Which set is the subset of the set
containing all the whole numbers?
( mathbf{A} cdot{1,2,3,4, dots dots .} )
в. {1}
( c cdot{0} )
D. All of the above
11
29 Given ( xi={x: x text { is a natural number }} ) ( A={x: x text { is an even number } x in N} ) ( mathrm{B}={mathrm{x}: mathrm{x} text { is an odd number, } mathrm{x} in mathrm{N}} )
Then ( (boldsymbol{B} cap boldsymbol{A})-(boldsymbol{x}-boldsymbol{A})=dots )
( A cdot phi )
в.
( c . B )
D. ( A-B )
11
30 The ( operatorname{set} A=x:|2 x+3|<7 ) is equal to
A. ( -10<2 x<4 )
в. ( -11<2 x<4 )
c. ( -12<2 x<4 )
D. ( -13<2 x<4 )
11
31 If ( S= )
( left{x in N: 2+log _{2} sqrt{x+1}>1-log _{1 / 2}right. )
then
( mathbf{A} cdot S=1 )
B. ( S=Z )
c. ( S=N )
D. none of these
11
32 Use the given Venn-diagram to find the
number of elements in ( A cup B )
11
33 Let ( boldsymbol{U} ) be the universal set and ( boldsymbol{A} cup boldsymbol{B} cup )
( C=U . ) Then
( {(boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{B}-boldsymbol{C}) cup(boldsymbol{C}-boldsymbol{A})}^{prime} ) is
equal to
A. ( A cup B cup C )
в. ( A cup(B cap C) )
c. ( A cap B cap C )
D. ( A cap(B cup C) )
11
34 Of 28 people in a park, 12 are children and the rest are adults. 8 people have to leave at ( 3 mathrm{pm} ; ) the rest do not. If, after 3
( mathrm{pm}, ) there are 6 children still in the park, how many adults are still in the park?
A . 14
B . 18
c. 15
D. 16
11
35 000
0
0
( infty )
00
11
36 A survey conducted on 600 students of
B. A part I classes of a collage gave the
following report. Out of 600 students,
307 took economics, 198 took history,
230 took sociology, 65 took history and
economics, 45 took economics and sociology, 31 took sociology and history and 10 took all the three subjects. The report sounded very impressive, but the surveyor was fired. Why?
11
37 Is the following pair of sets equal? Give
reasons.
( A={2,3}, B={x: x ) is a solution of
( left.boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}+boldsymbol{6}=mathbf{0}right} )
A. True
B. False
11
38 In an organization of pollution control board, engineers are represented by a
circle, legal experts by a square and
environmentalist by a triangle. Who is
most represented in the board as shown
in the figure?
A. Environmentalists
B. Engineers with legal background
c. Legal Experts
D. Environmentalists with Engineering background
11
39 If ( A Delta B=A cup B, ) then which of the
following can be correct?
A ( . A=B )
в. ( A cap B=phi )
( mathbf{c} cdot A Delta B=phi )
D. ( A Delta B=A sim B )
11
40 If ( boldsymbol{A}=(mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}), boldsymbol{B}=(mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}) ) and
( C={x: x in N: 2<x leq 7} ; ) find :
( B-C )
A ( cdot{4,6} )
в. {4,6,8}
c. {6,8,10}
D. {8,10}
11
41 Given, ( xi={ ) Natural numbers between ( 25 text { and } 45} ; A={text { even numbers }} ) and ( B )
( {text { multiples of } 3} ) then ( n(A)+n(B)= )
( boldsymbol{n}(boldsymbol{A} cup boldsymbol{B})+boldsymbol{n}(boldsymbol{A} cap boldsymbol{B}) . ) If true enter 1 else
0
11
42 State which of the following are finite
sets.
( (i){x: x in N} ) and ( (x-1)(x-2)=0 )
( (i i){x: x in N} ) and ( x ) is prime.
( (i i){x: x in N} ) and ( x ) is odd
A . (i) only
B. ( (i),(i i) ) and ( (i i i) )
c. ( (i) ) and ( (i i) )
D. (ii) and (iii)
11
43 Let ( boldsymbol{A}={1,2,3,4} ) and ( B={2,4,5,6} )
Find ( boldsymbol{A} cap boldsymbol{B} )
11
44 In a college of 300 students, every
student reads 5 newspapers and every
newspaper is read by 60 students. The number of newspapers is
A. at least 30
B. at most 20
c. exactly 25
D. none of these
11
45 In the Venn diagram, ( boldsymbol{xi} ) F UG cup ( boldsymbol{H} ). The
shaded region represents:
( mathbf{A} cdot G^{prime} cap F )
( mathbf{B} cdot(F cap H) cup G^{prime} )
( mathbf{c} cdot(F cap H) cap G^{prime} )
( mathbf{D} cdot(F cap G)^{prime} cap H )
11
46 If ( A=(6,7,8,9), B=(4,6,8,10) ) and ( C={x )
( boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq mathbf{7}} ; ) find :
( A-B )
A ( cdot{6,8} )
в. {7,9}
c. {6,9}
D. {6,7,9,10}
11
47 Verify whether ( boldsymbol{A} subset boldsymbol{B} ) for the sets ( boldsymbol{A}= )
( {{a, b, c}}, B={1,{a, b, c}, 2} )
11
48 (1979)
If X and Y are two sets, then X n(XUY) equals.
(a) x
(b) Y
(d) None of these.
11
49 Identify the type of set ( boldsymbol{A}={boldsymbol{x} mid boldsymbol{x} epsilon boldsymbol{R}, boldsymbol{2} leq boldsymbol{x} leq boldsymbol{3}} )
A. Finite Set
B. Infinite Set
c. Null set
D. singleton set
11
50 Which of the following has only one subset?
A ( cdot{0,1} )
B . {1}
( c cdot{0} )
( D cdot{} )
11
51 Let ( boldsymbol{A}={1,2,3,4,5,6} ) and ( B= )
( {6,7,8} . ) Find ( A triangle B ) and draw Venn
diagram
11
52 Let ( n ) be a positive integer. Call a non-
empty subset ( S ) of ( {1,2, ldots, n} ) good, if
the arithmetic mean of the elements of
( S, ) is also an integer. Further let ( t_{n} ) denote the number of good subsets of
( {1,2, ldots, n} . ) Prove that ( t_{n} ) and ( n ) are both
odd or both even
11
53 Statements:
(i) All rats are cats.
(ii) All cats are dogs.
Conclusions:
(i) All rats are dogs.
(ii) Some cats are rats.
A. Only conclusion I is true
B. Only conclusion Il is true
c. Both conclusion I and II are true
D. Neither conclusionl nor conclusion II is true
11
54 The diagram given below represents those students who play Cricket, Football and Kabaddi. Study the
diagram and identify the students who play all the three games.
( mathbf{A} cdot P+Q+R )
в. ( S )
( mathbf{c} cdot S+T+V )
D. ( V+T )
11
55 If ( mathbf{A}, mathbf{B} ) and ( mathbf{C} ) are three sets such that ( mathbf{A} cap mathbf{B}=mathbf{A} cap mathbf{C} ) and ( mathbf{A} cup mathbf{B}=mathbf{A} cup mathbf{C} )
then
A ( . A=B )
B. ( A=C )
c. ( mathrm{B}=mathrm{C} )
( mathbf{D} cdot A cap mathbf{B}=phi )
11
56 Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and
represent it by Venn diagram:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{5}, boldsymbol{4}, mathbf{7}} )
11
57 Let ( S={2,4,6,8, dots . .20} . ) What is the maximum number of subsets does ( boldsymbol{S} )
have ?
A . 10
B . 20
c. 512
D. 1024
11
58 In a town of 10,000 families it was
found that ( 40 % ) families buy newspaper ( A, 20 % ) buy newspaper ( B ) and ( 10 % ) buy newspaper ( C, 5 % ) families buy ( A ) and ( B ) ( 3 % ) buy ( B ) and ( C ) and ( 4 % ) buy ( A ) and ( C . ) If
( 2 % ) families buy all three newspapers, find number of families which buy None
of ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} )
11
59 In a survey it was found that 21 persons
liked product ( P_{1}, 26 ) liked product ( P_{2} )
and 29 liked product ( P_{3} ). If 14 persons
liked products ( P_{1} ) and ( P_{2} ; 12 ) persons
liked product ( P_{3} ) and ( P_{1} ; 14 ) persons
liked products ( P_{2} ) and ( P_{3} ) and 8 liked all
the three products. Find how many liked
product ( P_{3} ) only.
11
60 Draw the venn diagram to illustrate ( (boldsymbol{A} cup boldsymbol{B}) ) 11
61 Identify the type of ( operatorname{set} A^{prime}={1,2,6,7} )
and ( boldsymbol{B}={mathbf{6}, mathbf{1}, mathbf{2}, mathbf{7}, mathbf{7}} )
A. Overlapping Sets
B. Unequal Sets
c. Equal sets
D. None of these
11
62 ( lim _{x rightarrow 0} frac{1-cos (1-cos 2 x)}{x^{4}} ) 11
63 16. Out of 1865 people, 660 can
speak English and 1305 can
speak Marathi. But, 120 per-
sons can’t speak either lan-
guage. Then how many can
speak both languages?
(1) 220
(2) 440
(3) 120 (4) 1085
11
64 The Venn diagram shows the sets
( boldsymbol{xi}, boldsymbol{P}, boldsymbol{Q} ) and ( boldsymbol{R} ). Which of the following is
not true?
( mathbf{A} cdot P cap Q neq phi )
в. ( R subset Q )
( mathbf{c} cdot(P cap R) subset Q )
D. ( (P cap Q)=R )
11
65 The following table shows the percentage of the students of a school who participated in Election and Drawing competitions.

Competition Election Drawing
Percentage of Students
Draw a Venn diagram to represent this information and use it to find the
percentage of the students who
(i) Participated in Election only
(ii) Participated in Drawing only
(iii) Did not participate in any one of the competitions.

11
66 In the given figure, what percent of the circle is occupied by sector ( C ).
( 33 frac{1}{3} % )
( 22 frac{2}{9} % )
( 16 frac{2}{3} % )
11
67 All the students of a batch opted
Psychology, Business, or both. ( 73 % ) of
the students opted Psychology and ( 62 % ) opted Business. If there are 220
students, how many of them opted for both Psychology and business?
( mathbf{A} cdot 60 )
в. 100
c. 77
D. 35
11
68 If ( A ) and ( B ) are two disjoint sets and ( N ) is
the universal set then ( boldsymbol{A}^{c} cup )
( left[(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{c}right] ) is
( A cdot phi )
B. A
( c . ) в
D.
11
69 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{B}-boldsymbol{A} )
11
70 If ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi}, ) then relation between ( mathbf{A} )
and B is
This question has multiple correct options
( mathbf{A} cdot A neq B )
в. ( B subset A )
c. ( A subset B )
D. ( A=B )
11
71 State True or False.
The set represented by the
shaded portion of the following Venn-
diagram is: ( (B-A)^{prime} )
A. True
B. False
11
72 n the given diagram, the boys who are athletic and disciplined are indicated by which number?
( A )
3. 2
( c_{1} )
( D )
11
73 If ( boldsymbol{A}={boldsymbol{p}, boldsymbol{q}, boldsymbol{r}, boldsymbol{s}}, boldsymbol{B}={boldsymbol{r}, boldsymbol{s}, boldsymbol{t}, boldsymbol{u}}, ) then
( boldsymbol{A} / boldsymbol{B} ) is:
( A cdot(p, q) )
( B cdot{r, s} )
c. ( {t, u} )
D. ( {p, q, t, u} )
11
74 In a party, 70 guests were to be served tea or coffee after dinner. There were 52
guests who preferred tea while 37 preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee?
A . 15
B . 18
c. 19
D. 33
11
75 ( {a, b} ) is a subset of ( {b, c, a} ).If true
enter 1 else 0
11
76 Let ( boldsymbol{A}={1, mathbf{3}, mathbf{5}, mathbf{7}, dots .} ) and ( boldsymbol{B}= )
{1,2,3,4,5}
Then ( A ) and ( B ) are
A. Finite and infinite set respectively
B. Infinite and finite set respectively
c. Both Infinite sets
D. Both finite sets
11
77 From the given venn diagram, is ( boldsymbol{A} cap boldsymbol{B}^{prime} )
and ( A-B ) are equal. ( (text { Enter } 1 ) if true or
otherwise
11
78 Which of the following sets of real numbers is such that if ( x ) and ( y ) are the
elements of the set, then the sum of ( x )
and y is also an element of the set:
I. The set of negative integers
II. The set of rational numbers
III. The set of irrational numbers
A. None
B . I only
c. I and II only
D. Il and III only
E . I, II, and III
11
79 Let ( A={10,15,20,25,30,35,40,45} 50 )
( B={1,5,10,15,20,30} ) and ( C={1,5,15 )
( 20,35,45,3 . ) Verify ( A backslash(B cap C)=(A backslash )
( boldsymbol{B}) cup(boldsymbol{A} backslash boldsymbol{C}) )
11
80 What is the percentage of persons who read only two papers?
A ( .19 % )
(年 ( 1.1 % )
B. ( 31 % )
c. ( 44 % )
D. None of the above
11
81 State the following pair of sets
are equal or not
If they are equal then write 1 , else 0
( mathrm{E}=left{x: x^{2}+8 x-9=0right} ) and ( mathrm{F}={1,-9} )
11
82 For any two sets of ( A ) and ( B ), prove that ( boldsymbol{B}^{prime} subset boldsymbol{A}^{prime} Rightarrow boldsymbol{A} subset boldsymbol{B} ) 11
83 ( f(x)={x: x leq 10, x in N}, A={x: x geq 4} )
and ( mathrm{B}={x: 2<x<7} ; ) find the number
of equal sets.
11
84 Let ( P ) and ( Q ) be two sets then what is
( left(boldsymbol{P} cap boldsymbol{Q}^{prime}right) cup(boldsymbol{P} cup boldsymbol{Q})^{prime} ) equal to ( ? )
A ( cdotleft(P cap Q^{prime}right) cup(P cup Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi )
B . ( left(P cup Q^{prime}right) cup(P cup Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi )
C ( cdotleft(P cap Q^{prime}right) cup(P cap Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi )
D. none of the above
11
85 In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other
subjects. The class contains how many students?
A . 35
B. 42
( c .52 )
D. 60
11
86 Say true or false:
( A={x: x in N text { and } 5<x leq 6} ) is an
empty set.
A. True
B. False
11
87 If ( boldsymbol{A} cap boldsymbol{B}^{prime}=boldsymbol{phi}, ) then show that ( boldsymbol{A}=boldsymbol{A} cap )
( B ) and hence show that ( A sqsubseteq B )
11
88 luz
15 do TCE
B = An
ana
45. If A, B and C are three sets such that A
AUB= AUC, then
(a) A=C
(b) B=C
c) AB=
(d) A=B
[2009)
11
89 Given that ( boldsymbol{U}= )
( {3,7,9,11,15,17,18}, M= )
{3,7,9,11} and ( N={7,11,15,17} )
Find
(i) ( boldsymbol{M}-boldsymbol{N} )
(ii) ( boldsymbol{N}-boldsymbol{M} )
(iii) ( N^{prime}-M )
(iv) ( M^{prime}-N )
( (v) M cap(M-N) )
( (v i) N cup(N-M) )
(vii) ( boldsymbol{n}(boldsymbol{M}-boldsymbol{N}) )
11
90 set of rational numbers is ( left{-mathbf{6},-mathbf{5} frac{mathbf{3}}{mathbf{4}},-sqrt{mathbf{4}},-frac{mathbf{3}}{mathbf{5}},-frac{mathbf{3}}{mathbf{8}}, mathbf{0}, frac{mathbf{4}}{mathbf{5}}, mathbf{1}, mathbf{1} frac{mathbf{2}}{mathbf{3}}, mathbf{3}right. )
A. True
B. False
11
91 f ( n(A)=7, n(B)=8 ) then find the
maximum and minimum number of
elements of ( A U B )
11
92 Represent set ( A, B, C ) such that ( A subset ) ( boldsymbol{B}, boldsymbol{A} cap boldsymbol{C}=boldsymbol{phi} ) and ( boldsymbol{B} cap boldsymbol{C} neq boldsymbol{phi} ) by Venn
diagram. The number of separate
regions representing ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C}) )
is/are:
11
93 Let ( A={0,1,2,3,4}, B={1,-2,3,4,5,6} )
and ( C={2,4,6,7} )
(i) Show that ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} cup )
( boldsymbol{B}) cap(boldsymbol{A} cup boldsymbol{C}) )
(ii) Verify this relation using Venn diagram.
11
94 Let ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}} )
( boldsymbol{S}={(boldsymbol{a}, boldsymbol{b}) ; boldsymbol{a}, boldsymbol{b} in boldsymbol{A}, boldsymbol{a} text { divides } boldsymbol{b}}, ) write
down ( S ) explicitly
11
95 Which of the following Venn diagrams correctly represents Jaipur, Rajasthan, and India?
( A )
B.
( c )
D.
11
96 Find union of ( A ) and ( B, ) and represent it
using Venn diagram:
( boldsymbol{A}={1,2,3,4,5}, B={4,5,7,9} )
11
97 Classify ( D=left{x mid x=2^{n}, n in Nright} ) as
‘finite’ or ‘infinite’.
A . Infinite
B. Finite
c. Data insufficient
D. None of these
11
98 In a city, three daily newspapers ( A, B, C ) are published, ( 42 % ) read ( A ; 51 % ) read ( B ); ( 68 % ) read ( C ; 30 % ) read ( A ) and ( B ; 28 % ) read ( mathrm{B} ) and ( mathrm{C} ; 36 % ) read ( mathrm{A} ) and ( mathrm{C} ; 8 % ) do not read any of the three newspapers.
What is the percentage of persons who read only one paper?
( A .38 % )
в. ( 48 % )
( c .51 % )
D. None of the above
11
99 Verify: ( boldsymbol{A}^{prime} cap boldsymbol{B}=boldsymbol{B}-(boldsymbol{A} cap boldsymbol{B}) )
A. True
B. False
11
100 The shaded part of the figure is
( mathbf{A} cdot A cap B )
В. ( A cup B )
( c cdot A+B )
( mathbf{D} cdot cup-A )
11
101 Draw a Venn-diagram to show the
relationship between two overlapping sets ( A ) and ( B ). Now shade the region
representing ( boldsymbol{A} cap boldsymbol{B} )
11
102 In a group of 50 persons, 14 drink tea
but not coffee and 30 drink tea. Find
how many drink coffee but not tea?
11
103 Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3 2} )
11
104 35. Two sets A and B are as under :
A = {(a, b) € RXR :/ a -5/<1 and| b – 51<1};
B= {(a,b) € RXR:40a-6)2 +9(6-5)= 36}. Then :
[JEE M 2018]
(a) ACB
(b) AnB=0 (an empty set)
(c) neither ACB nor BCA
(d) BCA
11
105 The elements of ( boldsymbol{A} cap boldsymbol{B}^{prime} ) are: 11
106 Shade the region that represents the set
( boldsymbol{P} cap boldsymbol{Q}^{prime} ) in figure
11
107 ( boldsymbol{U}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}},left(boldsymbol{A}^{prime}right)={boldsymbol{b}, boldsymbol{d}, boldsymbol{f}} )
show that Venn diagram.
11
108 From the given diagram, find the
elements of:
( A-(B cap C) ) and ( (A-B) cup(A-C) ) and enter
1 or 0 respectively if the given relation
holds True or False: ( A-(B cap C)=(A-B) cup )
( (A-C) )
11
109 If ( A={1,2,3,4}, ) then the number of
subsets of ( A ) that contain the element 2
but not ( 3, ) is
A . 16
B. 4
c. 8
D. 24
11
110 Given ( A={x: x in N text { and } 3<x leq 6} )
and ( mathrm{B}={x: x in W text { and } x<4}, ) then
find ( : B-A )
11
111 f ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}} ) and ( boldsymbol{B}= )
( {3,5,7,9,11,13}, ) then find ( A-B ) and
( boldsymbol{B}-boldsymbol{A} )
11
112 The number of subsets of the ( operatorname{set} A= )
( left{a_{1}, a_{2}, dots dots dots a_{n}right} ) which contain even
number of elements is
A ( cdot 2^{n-1} )
B . ( 2^{n}-1 )
c. ( 2^{n}-2 )
D ( cdot 2^{n} )
11
113 ( 10 % ) of all aliens are capable of intelligent thought and have more than 3 arms, and ( 75 % ) of aliens with 3 arms or less are capable of intelligent thought. If ( 40 % ) of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms?
( mathbf{A} cdot 60 )
B. 70
c. 40
D. 45
11
114 Write all the subsets of the sets
( (i){a} )
( (i i) phi )
11
115 If ( A ) and ( B ) be two sets containing 4 and
8 elements respectively, what can be
the maximum number of elements in
( A cup B ? ) Find also, the minimum number
of elements in ( (boldsymbol{A} cup boldsymbol{B}) ) ?
A. Maximum number of elements ( =12 )
Minimum number of elements = 8
B. Maximum number of elements ( =14 ) Minimum number of elements ( =8 )
c. Maximum number of elements ( =12 )
Minimum number of elements = 9
D. Maximum number of elements ( =14 )
Minimum number of elements ( =7 )
11
116 Find ( A triangle B ) and draw Venn diagram
when:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}} ) and ( boldsymbol{B}={mathbf{2}, mathbf{4}} )
11
117 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{D} )
11
118 If ( boldsymbol{A}=left{boldsymbol{x} in boldsymbol{R}: boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x}-boldsymbol{7}<mathbf{0}right} ) and
( boldsymbol{B}=left{boldsymbol{x} in boldsymbol{R}: boldsymbol{x}^{2}+boldsymbol{9} boldsymbol{x}+mathbf{1 4}<mathbf{0}right}, ) then
which of the following is/are correct?
1. ( (boldsymbol{A} cap boldsymbol{B})=(-mathbf{2}, mathbf{1}) )
2. ( (boldsymbol{A} backslash boldsymbol{B})=(-mathbf{7},-mathbf{2}) )
Select the correct answer using the code given below:
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
11
119 In a town of 10,000 families it was found that ( 40 % ) families buy newspaper A, ( 20 % ) families buy newspaper ( B ) and 10
( % ) families buy newspaper ( C .5 % ) families buy A and B, 3% buy B and C
and ( 4 % ) buy ( A ) and ( C . ) If ( 2 % ) families buy
all the three newspaper, the member of families which buy A only is
11
120 Which of the following venn-diagrams
best represents the sets of females,
mothers and doctors?
( A )
B.
( c )
D.
11
121 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{C} )
11
122 The Venn diagram shows sets ( P, Q ) and ( R )
with regions labelled, I, II, III and IV.
State the region which represents set
( left[boldsymbol{P} cap(boldsymbol{Q} cup boldsymbol{R})^{prime}right] )
( A )
B.
( c . | )
D. IV
11
123 Define infinite set
Is ( {x: x in R: 1 leq x leq 3} ) a infinite
set?
A. True
B. False
11
124 If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= )
{3,5,7} and ( C={2,4} )
find ( : boldsymbol{A} times(boldsymbol{B}-boldsymbol{C}) )
Find the number of elements in such a
set.
11
125 ( f(1,2,3,4,5}, B={3,4,7,8} ) then find ( A cup )
( B ) and ( A cap B )
11
126 State whether the following statement is True or False
If ( boldsymbol{U}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}} ) and ( boldsymbol{A}= )
( {5,6,7}, ) then ( U ) is the subset of ( A )
A. True
B. False
11
127 Given, ( boldsymbol{A}={text { Triangles }}, boldsymbol{B}={ )
Isosceles triangles ( } ) ( C={text { Equilateral triangles }} . ) State
whether the following statements are correct or incorrect. Give reasons.
( A subset B )
11
128 ( X ) is a set of factors of 24 and ( Y ) is a set
of factors of ( 36, ) then find the sets ( X cup )
( boldsymbol{Y} ) and ( boldsymbol{X} cap boldsymbol{Y} )
11
129 In a class of 60 students, 45 students
like music, 50 students like dancing, 5 students like neither. Then the number
of students in the class who like both
music and dancing is
A . 35
B. 40
c. 50
D. 55
11
130 In a group of 15,7 have studied German, 8 have studied French, and 3 have not studied either. How many of these have
studied both German and French?
A . 0
B. 3
( c cdot 4 )
D. 5
11
131 Which of the following sets is not a
finite set?
( mathbf{A} cdotleft{(x, y): x^{2}+y^{2} leq 1 leq x+y, quad x, y in Rright} )
B ( cdotleft{(x, y): x^{2}+y^{2} leq 1 leq x+y, quad x, y in Zright} )
( mathbf{c} cdotleft{(x, y): x^{2} leq y leq|x|, quad x, y in Zright} )
D. ( left{(x, y): x^{2}+y^{2}=1, x, y in Zright} )
11
132 Let ( S ) be the set of all values of ( x ) such
( operatorname{that} log _{2 x}left(x^{2}+5 x+6right)<1 ) then the
sum of all integral value of ( x ) in the set
S, is
( A cdot O )
B. 8
( c cdot s )
D. 10
11
133 If ( A, B ) and ( C ) are three finite sets then
what is ( [(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{C}]^{prime} ) equal to?
A ( cdotleft(A^{prime} cup B^{prime}right) cap C^{prime} )
B ( cdot A^{prime} capleft(B^{prime} cap C^{prime}right) )
c. ( left(A^{prime} cap B^{prime}right) cup C^{prime} )
D. ( (A cap B) cap C )
11
134 Draw Venn diagrams to illustrate ( boldsymbol{C} cap )
( (B backslash A) )
11
135 The following sets are equal. ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{N} ; mathbf{1}<boldsymbol{x}<mathbf{4}} ) and
( B=left{x: x text { is a solution of } x^{2}+5 x+right. )
( mathbf{6}=mathbf{0}} )
A . True
B. False
11
136 f ( A={a, b}, B={x, y} ) and ( C= )
( {a, c, y}, ) then verify that ( A times )
( (boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} times boldsymbol{B}) cap(boldsymbol{A} times boldsymbol{C}) )
11
137 State true or false:
A set of rational number is a subset of a
set of real numbers
A. True
B. False
11
138 The Venn diagram shows sets ( boldsymbol{xi}, mathrm{P} ) and
( Q )
The shaded region in the Venn diagram
represents set:
( A cdot P cap Q )
в. ( P^{prime} cap Q )
c. ( P cap Q^{prime} )
D. ( P^{prime} cap Q^{prime} )
11
139 If a set contains ( n ) elements then
number of elements in its power set is
A ( cdot 2^{n}-n )
B . ( 2^{n}-2 )
( c cdot 2^{n} )
( mathbf{D} cdot n^{2} )
11
140 If ( boldsymbol{A}=left{4^{n}-3 n-1: n in Nright} ) and ( B= )
( {9(n-1): n in N}, ) then?
( mathbf{A} cdot B subset A )
B. ( A cup B=N )
c. ( A subset B )
D. None of these
11
141 ( A subset B ) then show that ( A cap B ) and ( A backslash )
( B ) (use Venn diagram)
11
142 Suppose ( boldsymbol{U}= )
( {3,4,5,6,7,8,9,10,11,12,13}, A= )
( {3,4,5,6,9}, B={3,7,9,5} ) and ( C= )
( {6,8,10,12,7} . ) Write down the
following set and draw Venn diagram for
( boldsymbol{B}^{prime} )
11
143 Looking at the Venn diagram list the
elements of the following sets:
( boldsymbol{B} backslash boldsymbol{C} )
11
144 If ( boldsymbol{P}={boldsymbol{x} mid mathbf{2 4}<boldsymbol{x}<mathbf{3 0}} ) and ( boldsymbol{Q}= )
( {boldsymbol{x} mid mathbf{2 5}<boldsymbol{x}<mathbf{3 2}}, ) prove that ( boldsymbol{P}-boldsymbol{Q} neq )
( boldsymbol{Q}-boldsymbol{P} )
11
145 If ( A, B ) and ( C ) are three sets such that
( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} cap boldsymbol{C} ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cup boldsymbol{C} )
then
A ( . A=C )
B. ( B=C )
c. ( A cap B=phi )
D. ( A=B )
11
146 Find union of ( A ) and ( B ), and represent it
using Venn diagram:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{4}, mathbf{5}, mathbf{6}} )
11
147 Find the following set is singleton set or
not.
( mathrm{B}={boldsymbol{y}: 2 boldsymbol{y}+1<3 text { and } boldsymbol{Y} boldsymbol{epsilon} boldsymbol{W}} )
11
148 Find union of ( A ) and ( B ) by representing
using Venn diagram:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}}, boldsymbol{B}={boldsymbol{b}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} )
( mathbf{A} cdot{a, b, c, d} )
B ( cdot{b, d, e, f} )
( mathbf{c} cdot{b, d} )
D. None of these
11
149 ( 40 % ) of all high school students hate
roller coasters; the rest love them. ( 20 % )
of those students who love roller
coasters own chinchillas. What
percentage of students love roller
coasters but do not own a chinchilla?
A . 45
B . 30
c. 50
D. 48
11
150 Let ( n(cup)=700, n(A)=400, n(B)=300, n(A cap )
( mathrm{B})=300 . ) Then ( left(mathrm{A}^{prime} cap mathrm{B}^{prime}right)= )
A . 300
B. 400
( c . ) 350
D. 250
11
151 How many took ‘soup’ 11
152 Stat whether the following pairs of sets
are equal or not
(I) ( A={x: x text { is a letter of the world ‘paper’ }} ) and ( A=operatorname{set} ) of digits in the number 59672
(ii) ( A={x: x text { is a letter of the world ‘pepar’ }} ) and ( mathrm{B}=operatorname{set} ) of digits in the number 756889
11
153 Find ( A triangle B ) and draw Venn diagram when:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}} ) and ( boldsymbol{B}={boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} )
11
154 The Venn diagram shows sets ( xi, P ) and
( Q )
The shaded region in the Venn diagram
represents set
( A cdot P cap Q )
в. ( P^{prime} cap Q )
c. ( P cap Q^{prime} )
D. ( P^{prime} cap Q^{prime} )
11
155 Let ( A, B, C ) be the subsets of the
universal set ( X ) Let ( A^{prime} B^{prime} C^{prime} ) denote their
complements in X Then which of below
corresponds to the shaded portion in
the given figure
( mathbf{A} cdot A^{prime} cap B cap C )
B ( cdot A cap B^{prime} cap C )
c. ( A cap B cap C^{prime} )
( mathbf{D} cdot A^{prime} cap B^{prime} cap C )
11
156 ( P, Q ) and ( R ) are three sets and ( xi P cup Q cup )
( R . ) Given that ( n(xi)=60, n(P cap Q)=5 )
( n(Q cap R)=10, n(p)=20 ) and ( n(Q)=23 )
find ( nleft(P^{prime} cup Qright) )
A. 37
3. 38
( c cdot 45 )
D. 52
11
157 Find ( A triangle B ) and draw Venn diagram
when:
( boldsymbol{A}={1,4,7,8} ) and ( boldsymbol{B}={4,8,6,9} )
11
158 State whether the following statement is True or False
( A={x mid x text { is a negative integer } ; x> )
-5} is a finite set.
A. True
B. False
11
159 Draw Venn diagrams to illustrate ( (boldsymbol{A} cup )
( boldsymbol{B}) backslash(boldsymbol{A} cup boldsymbol{C}) )
11
160 Draw Venn diagrams to illustrate ( boldsymbol{C} cap )
( (boldsymbol{B} cup boldsymbol{A}) )
11
161 The shaded part of the given figure is
represented as
( A cdot A cap B )
в. ( A cup B )
( c cdot A-B )
D. All of the above
11
162 If the following statement is true, enter
1 or else 0.

The set of even natural numbers less
than 21 and the set of odd natural
numbers less than 21 have equal
number of elements and are termed as
equivalent sets.

11
163 8.
Let P = {0: sin 0 — cos 0 – 2 cos) and
Q= {0: sin + cos 0 – 2 sin 0; be two sets. Then (2011)
(a) P Q and 0-P (b) P
(c) P Q
(d) P=0
11
164 Draw Venn diagrams to illustrate ( boldsymbol{A} cap ) ( (B backslash C) ) 11
165 The set of letters needed to spel
“CATARACT” and the set of letter needed
to spell “TRACT” are equal
A. True
B. False
11
166 Let ( n ) be a natural number and ( X= )
( {1,2, dots dots, n} . ) For subsets ( A ) and ( B ) of
( X, ) we denote ( A Delta B ) to be the set of all
those elements of ( X ) which belong to
exactly one of ( A ) and ( B . ) Let ( F ) be a
collection of subsets of ( X ) such that for
any two distinct elements ( A ) and ( B ) in ( F )
the ( operatorname{set} A Delta B ) has at least two elements.
Show that ( F ) has at most ( 2^{n-1} ) elements
Find all such collections ( boldsymbol{F} ) with ( mathbf{2}^{n-1} )
elements.
11
167 If ( boldsymbol{X}={1,2,3,4,5,6,7,8,9,10} ) is the
universal set and ( boldsymbol{A}={1,2,3,4}, B= )
( {2,4,6,8}, C={3,4,5,6} ) verify the
following.
(a) ( boldsymbol{A} cup(boldsymbol{B} cup boldsymbol{C})=(boldsymbol{A} cup boldsymbol{B}) cup boldsymbol{C} )
( (b) A cap(B cup C)=(A cap B) cup(A cap C) )
(c) ( left(boldsymbol{A}^{prime}right)^{prime}=boldsymbol{A} )
A. Only a is true
B. Only b and c are true
c. only a and b are true
D. All three a, b and c are true.
11
168 Let ( boldsymbol{P}= ) Set of all integral multiples of 3
( ; Q=operatorname{set} ) of integral multiples of ( 4 ; R= ) Set of all integral multiples of 6 Consider the following relations:
( mathbf{1} boldsymbol{P} cup boldsymbol{Q}=boldsymbol{R} )
( mathbf{2} . boldsymbol{P} subset boldsymbol{R} )
3. ( boldsymbol{R} subset(boldsymbol{P} cup boldsymbol{Q}) )
Which of the relations given above is/are correct ?
A. only 1
B . only 2
c. only 3
D. both 2 and 3
11
169 Let ( boldsymbol{E}=left{boldsymbol{x}: boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-boldsymbol{6}=boldsymbol{0}right} ) and
( boldsymbol{F}={-mathbf{6}, mathbf{1}} . ) Then
A ( . E=F )
в. ( E neq F )
c. ( E subset F )
D. ( F subset E )
11
170 Let ( A, B ) are two sets such that ( n(A)= ) ( mathbf{6}, boldsymbol{n}(boldsymbol{B})=mathbf{8} ) then the maximum number
of elements in ( n(A cup B) ) is
A. 7
B. 9
c. 14
D. None
11
171 Directions : From among the giv-
en alternatives select the one in which
the set of numbers is most like the set
of numbers given in the question.
10. Given set : (2, 10, 28)
(1) (4, 20, 56)
(2) (7, 42, 49)
(3) (12, 24, 48)
(4) (9, 27, 81)
11
172 State whether the given set is finite or
infinite :Enter 1 for Finite and 0 for
infinite
( A={x: x in Z text { and } x<10} )
11
173 State whether the set is finite or
infinite:
The set of points on a line
11
174 The sets ( A={text { letters of the world ‘FLOW’ }} ) and ( mathrm{B}={text { letters of the word ‘FOLLOW’ }} )
are :
A. Equivalent sets
B. Equal sets
c. singleton sets
D. Null sets
11
175 Let ( boldsymbol{A}={1,2,3,4} ) and ( B={2,4,6,8} )
Then find ( boldsymbol{A}-boldsymbol{B} )
11
176 Use the given figure to find ( : boldsymbol{n}left(boldsymbol{B}^{prime} cap boldsymbol{A}right) )
Given, ( n(xi)=52, n(A)=43 ) and
( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} )
11
177 8 have studied French and 3 have not
studied either. The Venn diagram
showing the number of students who
have studied both is :
( mathbf{A} )
B.
( c )
( D )
11
178 Which of the following Venn diagrams
correctly represents persons, trees and
environment?
( A )
B.
( c )
D.
11
179 In a survey of 100 persons it was found that 28 read magazine ( A, 30 ) read magazine B, 42 read magazine ( C, 8 ) read magazines ( A ) and ( B, 10 ) read magazines A and ( mathrm{C}, 5 ) read magazines ( mathrm{B} ) and ( mathrm{C} ) and 3 read all the three magazines. Find how many read none of three magazines? 11
180 Classify ( C={ldots,-3,-2,-1,0} ) as
‘finite’ or ‘infinite’.
A . Infinite
B. Finite
c. Data insufficient
D. None of these
11
181 In a battle ( 70 % ) of the combatants lost
one eye, ( 80 % ) an ear, ( 75 % ) an arm, ( 85 % ) a
leg, ( x % ) lost all the four limbs the
minimum value of ( x ) is
A . 10
B. 12
c. 15
D.
11
182 If ( A ) and ( B ) are non-empty sets such that
( A supset B, ) then
( mathbf{A} cdot B^{prime}-A^{prime}=A-B )
B ( cdot B^{prime}-A^{prime}=B-A )
( mathbf{C} cdot A^{prime}-B^{prime}=A-B )
D ( cdot A^{prime} cap B^{prime}=B-A )
E ( cdot A^{prime} cup B^{prime}=A^{prime}-B^{prime} )
11
183 In Venn diagram given:
( mathbf{A} cdot A cup B=0 )
В ( . A cup B=mu )
( mathbf{c} cdot A cap B=mu )
D. ( A cap B=phi )
11
184 Let ( A_{1}, A_{2} ) and ( A_{3} ) be subsets of a set ( X )
Which one of the following is correct?
A. ( A_{1} cup A_{2} cup A_{3} ) is the largest subset of ( X ) containing
elements of each of ( A_{1}, A_{2} ) and ( A_{3} )
B. ( A_{1} cup A_{2} cup A_{3} ) is the smallest subset of ( X ) containing
either ( A_{1} ) or ( A_{2} cup A_{3} ) but not both
C. The smallest subset of ( X ) containing ( A_{1} cup A_{2} ) and ( A_{3} )
equals the smallest subset of ( X ) containing both ( A_{1} ) and ( A_{2} cup A_{3} ) only if ( A_{2}=A_{3} )
D. None of these
11
185 If ( A_{1}, A_{2}, dots, A_{100} ) are sets such that ( boldsymbol{n}left(boldsymbol{A}_{boldsymbol{i}}right)=boldsymbol{i}+boldsymbol{2}, boldsymbol{A}_{1} subset boldsymbol{A}_{2} subset boldsymbol{A}_{3} ldots ldots . . boldsymbol{A}_{100} )
and ( bigcap_{i=3}^{100} A_{i}=A, ) then ( n(A)= )
( A cdot 3 )
B. 4
( c .5 )
D. 6
11
186 If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= )
( {mathbf{3}, boldsymbol{5}, boldsymbol{7}} ) and ( boldsymbol{C}={mathbf{2}, boldsymbol{4}} )
find ( : boldsymbol{n}(boldsymbol{A}-boldsymbol{B}) )
11
187 In a town of 10000 families, it was found
that ( 40 % ) families buy a newspaper ( A ) ( 20 % ) families buy newspaper ( B ) and ( 10 % ) families buy newspaper C. 5% families buy both ( A ) and ( B, 3 % ) buy ( B ) and ( C ) and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only.
A . 3300
в. 3500
( c .3600 )
D. 3700
11
188 Which of the following is a singleton
set?
A. ( {x:|x|=5, x in N} )
B . ( {x:|x|=6, x in Z} )
c. ( left(x: x^{2}+2 x+1=0, x in Nright) )
D. ( left{x: x^{2}=7, x in Nright} )
11
189 Mark the correct alternative of the
following.
For any ( operatorname{set} A,left(A^{prime}right)^{prime} ) is equal to?
A ( cdot A^{prime} )
B. A
( c cdot phi )
D. None of these
11
190 Find union of ( A ) and ( B ) by representing
using Venn diagram:
( boldsymbol{A}={1,2,3,4,8,9}, B={1,2,3,5} )
( mathbf{A} cdot{1,2,3,4,5,8,9} )
B . {1,2,3}
( mathbf{c} cdot{1,2,3,4,8,9} )
D. None of these
11
191 sets of students who have opted for
Mathematics (M) physics (P) Chemistry
(C) and Electronics (E)
What does the shaded region represent
A. Students who oped for Physic, Chemistry and Electronics
B. Students who oped for Mathematics, Physics
Chemistry
c. Students who opted for Mathematics, Physics and Electronics
D. Students who opted for Mathematics, Chemistry and ectron
11
192 Use the given figure to find :
Given, ( n(xi)=52, n(A)=43 ) and
( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} )
( nleft(B^{prime}right) )
11
193 From a survey of 100 college students, a marketing research company found
that 75 students owned stereos, 45
owned cars, and 35 owned cars and stereos. How many students owned either a car or a stereo?
A . 85
B. 47
( c .68 )
D. None of these
11
194 ( boldsymbol{n}(boldsymbol{A} cap boldsymbol{B}) ) 11
195 In a group of 1000 people, there are 750 who can speak Hindi and 400 who can
speak Bengali. How many can speak Bengali ?
11
196 Say true or false:
( mathrm{C}={text { even numbers between } 6 text { and } 10} ) is
not an empty set.
A. True
B. False
11
197 Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and
represent it by Venn diagram:
( boldsymbol{A}={1,2,4,5}, B={2,5,7,9} )
11
198 State whether the following sets are
finite or infinite
(i) ( A={x: x text { is a multiple of } 5, x in mathbb{N}} )
(ii) ( B={x: x ) is an even prime
number
(iii) The set of all positive integers
greater than 50
11
199 f ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1} boldsymbol{0}) ) and
( C={x: x in N: 2<x leq 7} ; ) find :
( boldsymbol{B}-(boldsymbol{A} cap boldsymbol{C}) )
The sum of the elements in the above
( operatorname{set} ) is?
11
200 What does the shaded region represent in the figure given below?
A ( cdot(P cup Q)-(P cap Q) )
В . ( P cap(Q cup R) )
( mathbf{c} cdot(P cap Q) cap(P cap R) )
D ( cdot(P cap Q) cup(P cap R) )
11
201 Draw Venn diagrams to illustrate ( boldsymbol{A} cap )
( B^{prime} )
11
202 Let ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{N}, mathbf{1}<boldsymbol{x} leq mathbf{3}} ) and
( boldsymbol{B}=left{boldsymbol{y}: boldsymbol{y}^{2}-mathbf{5} boldsymbol{y}+boldsymbol{6}=mathbf{0}right}, ) then
A ( . A subset B )
в. ( B subset A )
( mathbf{c} cdot A=B )
D. ( A neq B )
11
203 The set of all values of ( ^{prime} x^{prime} ) satisfying the inequation ( left(frac{1}{|x|-3}right) leq frac{1}{2} ) is
A ( (-infty,-5) cup(-3,3) cup[5, infty) )
B . ( (-infty,-5] cup[-3,3] cup[5, infty) )
c. ( (-infty,-5) cup(-3,3) cup(5, infty) )
D. None of the above
11
204 If universal set ( boldsymbol{xi}= )
( {a, b, c, d, e, f, g, h}, A= )
( {b, c, d, e, f}, B={a, b, c, g, h} ) and
( C={c, d, e, f, g}, ) then find ( B-A )
( mathbf{A} cdot{b, c, e, f} )
в. ( {a, b, f, h} )
( c cdot{a, g, h} )
D. ( {a, c, e, g} )
11
205 Given the set ( P ) is the set of even
numbers between 15 and ( 25 . ) Label a
Venn diagram to represent the set ( boldsymbol{P} )
and indicate all the elements of set ( boldsymbol{P} )
in the Venn diagram.
B . {16,20,24}
c. {16,18,20,22,24}
D. None of these
11
206 f ( x={a, b, c, d} ) and ( y={b, d, g, f} )
find ( boldsymbol{x}-boldsymbol{y} ) and ( boldsymbol{y}-boldsymbol{x} )
Draw the appropriate venn diagram for
( boldsymbol{A}^{prime} cap boldsymbol{B}^{prime} )
11
207 Eighty-nine students of class VIII appeared for a combined test in Maths
and Physics. If 62 students passed in
both ( ; 4 ) failed in Maths and Physics and
7 failed only in Maths. Use a Venndiagram to find: how many passed in Maths.
11
208 Draw Venn diagrams to illustrate ( (A cup )
( B)^{prime} )
11
209 If ( A ) and ( B ) are two disjoint sets and ( N ) is
universal set, then ( boldsymbol{A}^{circ} cupleft[(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{circ}right] )
is
( A cdot phi )
в. ( A )
( c . B )
D. ( N )
11
210 000
0
0
( infty )
00
11
211 From the diagram, relation between ( A ) and B……. 11
212 If ( boldsymbol{A}=left{(boldsymbol{x}, boldsymbol{y}) mid boldsymbol{x}^{2}+boldsymbol{y}^{2} leq mathbf{4}right} ) and ( boldsymbol{B}= )
( left{(x, y) mid(x-3)^{2}+y^{2} leq 4right} ) and the
point ( Pleft(a, a-frac{1}{2}right) ) belongs to the set ( B-A, ) then the set of possible real
values of ( a ) is
( ^{mathrm{A}} cdotleft(frac{1+sqrt{31}}{4}, frac{7+sqrt{7}}{4}right] )
в. ( left[frac{7-sqrt{7}}{4}, frac{1+sqrt{31}}{4}right) )
( ^{c} cdotleft(frac{1-sqrt{31}}{4}, frac{7-sqrt{7}}{4}right] )
D. None of the above
11
213 The number of subsets of the set
{10,11,12} is
( A cdot 3 )
B. 8
( c cdot 6 )
D. 7
11
214 Let ( boldsymbol{A}={-mathbf{7}, mathbf{5}, mathbf{2}} ) and ( boldsymbol{B}= )
( {sqrt[3]{125}, sqrt{4}, sqrt{49}} )
Are the sets ( A ) and ( B ) equal? Choose the correct option for the above. Justify
your answer.
A. Yes
B. No
c. Ambiguous
D. Data insufficient
11
215 begin{tabular}{l}
( infty ) \
hline 00 \
hline 0 \
hline( infty )
end{tabular}
11
216 In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?
A . 0
B . 2
( c .3 )
D.
11
217 Given ( A={x: x in N text { and } 3<x leq 6} )
and ( mathrm{B}={x: x in W text { and } x<4}, ) then
find ( : A-B )
11
218 The numbers representing ( boldsymbol{A} cap boldsymbol{B} ) are 11
219 ( P cup Q ) and ( P cap Q ) 11
220 The number of subsets ( boldsymbol{R} ) of ( boldsymbol{P}= )
( (1,2,3, dots, 9) ) which satisfies the
property “There exit integers ( mathbf{a} in mathbf{R}, mathbf{b} in ) ( mathbf{R}, mathbf{c} in mathbf{R}^{prime prime} ) is
A .512
в. 466
c. 467
D. None of these
11
221 An investigator interviewed 100
students to determine their preferences for the three drinks milk coffee and tea.
He reported the following, 10 students had all the three drinks, 20 had milk
and coffee, 30 had coffee and tea ( , 25 )
had milk and tea, 12 had milk only. 5
had coffee only, 8 had tea only. The
number of students that did not take
any of the three drinks is.
11
222 Is ( A^{prime} cup B^{prime}=(A cap B)^{prime} ) ? Also, verify if ( A^{prime} cap B^{prime} )
( =(A cup B)^{prime} )
A. Yes
B. No
( c ). Can’t Say
D. Cannot be determined
11
223 ( (boldsymbol{P} cap boldsymbol{Q}) cup(boldsymbol{Q} cap boldsymbol{R}) )
A ( cdot{b, c, f} )
в. ( {b, c, d} )
( mathbf{c} cdot{b, c, d, f} )
( mathbf{D} cdot{b, c, f, g} )
11
224 For any three sets, ( A B ) and ( C, B backslash(A cup )
( C) ) is:
( mathbf{A} cdot(A backslash B) cap(A backslash C) )
B . ( (B backslash A) cap(B backslash C) )
c. ( (B backslash A) cap(A backslash C) )
D. ( (A backslash B) cap(B backslash C) )
11
225 ( mathbf{f} boldsymbol{A}={mathbf{6}, mathbf{9}, mathbf{1 1}} ) and ( boldsymbol{B}=boldsymbol{phi} ),find ( boldsymbol{A} cup boldsymbol{B} ) 11
226 ( A ) and ( B ) are two sets having 3 elements in common.ff ( n(mathbf{A})=mathbf{5}, n(mathbf{B})=mathbf{4} ) then
Find
( boldsymbol{n}(boldsymbol{A} times boldsymbol{B}) boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{n}[(boldsymbol{A} times boldsymbol{B}) cap(boldsymbol{B} times boldsymbol{A})] )
11
227 Find total number of subsets of ( A={5,7} ) 11
228 ( operatorname{Set} boldsymbol{U}={1,2, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}}, boldsymbol{A}= )
( left{x: x in N, 30 leq x^{2} leq 70right}, B={x: x )
is a prime number ( <10} . ) Which of the
following does NOT belong to the set
( (A-B)^{prime} ? )
( mathbf{A} cdot mathbf{4} )
B. 5
( c cdot 6 )
D.
11
229 Which of the following are examples of
the null
Set of all even prime numbers.
A. True
B. False
11
230 List all of the subsets of the set
( {a, b, c, d} )
11
231 Using properties of sets, prove that ( boldsymbol{A} cup ) ( (boldsymbol{A} cap boldsymbol{B})=boldsymbol{A} ) 11
232 Use the Venn diagram to answer the
following questions
(i) List ( U, G ) and ( H )
(ii) Find ( G^{prime}, H^{prime}, G^{prime} cap H^{prime}, n(G cup H)^{prime} ) and
( boldsymbol{n}(boldsymbol{G} cap boldsymbol{H})^{prime} )
11
233 Write down the set represented by the
shaded region in figure (ii)
11
234 The Venn diagram shows the sets
( xi, P, Q ) and ( R . ) Which of the following is
not true?
( mathbf{A} cdot P cap Q neq emptyset )
в. ( R subset Q )
( mathbf{c} cdot(P cap R) subset Q )
D. ( (P cap Q)=R )
11
235 In the Venn diagram, the numbers
represent the number of elements in the
subsets. Given that
( boldsymbol{xi}=boldsymbol{F} cup boldsymbol{G} cup boldsymbol{H} ) and ( boldsymbol{n}(boldsymbol{xi})=mathbf{4 2}, ) find
( nleft(G^{prime} cup Hright) )
( A cdot 18 )
3. 28
( c .30 )
0.38
11
236 Use Venn diagrams to verify De’Morgan’s law of complementation
( (boldsymbol{A} cup boldsymbol{B})^{prime}=boldsymbol{A}^{prime} cup boldsymbol{B}^{prime} )
11
237 Is the following statement True or False?
( (boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{B}-boldsymbol{A})=(boldsymbol{A} cup boldsymbol{B}) cap )
( left(A^{prime} cup B^{prime}right) )
If True then write answer as 1
If False then write answer as 0
11
238 If ( boldsymbol{T}= )
( {x: x text { is a letter in the word ‘TEETH’ }} )
find all its subsets.
11
239 Find ( n(B-C)^{c} ) 11
240 If ( X ) and ( Y ) are two sets, then ( X cap(Y cup )
( X)^{prime} ) equals
( mathbf{A} cdot X )
в. ( Y )
( c cdot phi )
D. None of these
11
241 Let ( P ) be the set of points inside the
square, ( Q ) be the set of points inside the triangle and ( R ) be the set of points
inside the circle. If the triangle and circle intersect each other and are
contained in the square then,
This question has multiple correct options
A. ( P cap Q cap R neq phi )
в. ( P cup Q cup R=R )
c. ( P cup Q cup R=P )
D. ( P cup Q=R cup P )
11
242 If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= )
( {boldsymbol{3}, boldsymbol{5}, boldsymbol{7}} ) and ( boldsymbol{C}={mathbf{2}, boldsymbol{4}} ; ) find :
( boldsymbol{B}-boldsymbol{C} )
11
243 There are 60 students in a class. Every student learns at least one of the
subjects Kannada or English. 45
students offer Kannada and 30 English.
How many students offer both the
subjects? Draw Venn diagram.
11
244 If universal set ( boldsymbol{xi}= ) ( {boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}, boldsymbol{h}}, boldsymbol{A}= )
( {b, c, d, e, f}, B={a, b, c, g, h} ) and
( boldsymbol{C}={boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}} ) find ( : boldsymbol{C}-(boldsymbol{B} cap boldsymbol{A}) )
Thus find the number of elements in the above set.
11
245 fin ( (A)=120, N(B)=250 ) and ( n(A-B)= )
52, then find ( n(A cup B) )
A . 302
B. 250
( c .368 )
D. None of the above
11
246 Examine whether ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} ) is a
positive integer divisible by ( 3} ) is a subset of ( B={x: x text { is a multiple of } 5 )
( boldsymbol{x} in boldsymbol{N}} )
11
247 Use the given Venn-diagram to find: B –
4
3. 10
( c )
P
11
248 The Venn diagram shows the
relationship between sets ( xi, P, Q ) and ( R )
The shaded region in the diagram
represents set:
( A cdot(P cap R) cap Q )
B . ( left(P cap R^{prime}right) cap Q^{prime} )
( mathrm{c} cdotleft(P cap R^{prime}right) cap Q )
( mathrm{D} cdot Q^{prime} cap R^{prime} )
11
249 00
00
00
00
11
250 State whether the set is finite or
infinite:

The set of all schools in this world

11
251 If ( boldsymbol{A}=(mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}), boldsymbol{B}=(mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}) ) and
( C={x: x in N: 2<x leq 7} ; ) find :
( boldsymbol{B}-boldsymbol{B} )
( A cdot phi )
B . {0}
c. {6,7}
D. {4}
11
252 Let ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}}, boldsymbol{B}={mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}} )
Find ( boldsymbol{A}-boldsymbol{B} ) and ( boldsymbol{B}-boldsymbol{A} )
11
253 The following is an example of empty
set:
( {x: x ) is a point common to any two
parallel lines
A. True
B. False
11
254 If ( A ) has 2 elements and ( B ) has 2
elements, then the number of elements
( operatorname{in} B times A ) is :
11
255 If ( boldsymbol{A}={mathbf{2}, mathbf{4}{mathbf{5}, mathbf{6}}, mathbf{8}}, ) then which one of
the following statements is not correct?
( mathbf{A} cdot{5,6} subseteq A )
( mathbf{B} cdot{5,6} in A )
c. {2,4,8}( subseteq A )
D. ( 2,4,8 in A )
11
256 Prove that: ( 1 . P(1,1)+2 . P(2,2)+ )
( 3 . P(3,3)+ldots+n . P(n, n)= )
( P(n+1, n+1)-1 )
11
257 Let ( boldsymbol{A}={1,2,3, dots, 10} ) and ( B= )
( {101,102,103, dots, 1000} . ) Then set ( A )
and ( B ) are
A. Both finite sets
B. Infinite and finite set respectively
c. Both Infinite sets
D. Finite and infinite set respectively
11
258 f ( M={b, h, i} ; N={b, c, d, e} ) and
( s={e, f, g}, ) determine ( M cap N cap S )
and represent it in a venn diagram.
11
259 The ( (boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}) capleft(boldsymbol{A} cap boldsymbol{B}^{C} cap boldsymbol{C}^{C}right)^{C} cap )
( C^{c} ) is equal to
( mathbf{A} cdot B^{C} cap C^{C} )
в. ( A cap C )
( c cdot B cap C^{c} )
D. ( C cap C^{c} )
11
260 f ( A=1,3,5, dots dots dots 17 ) and ( B= )
( 2,4,6, dots dots 18 ) and ( N( ) the set of natural
numbers) is the universal set, then
show that ( boldsymbol{A}^{prime} cupleft((boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{prime}right)=boldsymbol{N} )
11
261 If ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{7}, mathbf{9}}, boldsymbol{B}= )
( {mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}} ) then ( boldsymbol{B}-boldsymbol{A}= )
11
262 If ( A subset B ) then show that ( A cup B=B )
(use Venn diagram)
11
263 Classify ( B={y mid y text { is a factor of } 13} ) as
‘finite’ or ‘infinite’.
A . Infinite
B. Finite
c. Data insufficient
D. None of these
11
264 Statements
(i) Some chalks are chairs
(ii) Some chairs are tables. Conclusions:
I. Some chalks are tables.
II. Some tables are chalks.
A. Only conclusion lis true
B. Only conclusion II is true
c. Both conclusions I and II are true
D. Neither conclusion I nor conclusion II is true
11
265 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{C}-boldsymbol{A} )
11
266 State the following statement is True or False
( boldsymbol{D}=left{boldsymbol{y} mid boldsymbol{y}=boldsymbol{3}^{n}, boldsymbol{n} in boldsymbol{N}right} ) is an example
of an infinite set.
A. True
B. False
11
267 (0)
THU
59. If X = {4″ – 3n-1: neN
: neN} and Y = {9(n-1):n € N},
and Ya
N is the set of natural numbers, then X UY is equal
to:
[JEE M 2014)
(a) x (6) y (0) N (d) Y-X
1 members is
11
268 Of 30 applicants for a job, 14 had at least 4 years’experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least
4 years’ experience and a degree?
A . 14
B. 13
c. 9
( D .7 )
E. 5
11
269 6. Let P = {0: sin 0 – cos e = V cos 8; and Q = {0: sin e
+ cos 0 = V2 sin 8} be two sets. Then
a. P(Q and Q-P+º) b. QxP
c. PxQ
b d. P=Q (IIT-JEE 2011)
11
270 ( boldsymbol{n}[boldsymbol{P}(boldsymbol{A})]=boldsymbol{n}[boldsymbol{P}(boldsymbol{B})], ) then ( A ) and ( mathrm{B} ) are
sets
A . Equal
B. Overlapping
c. Equivalent
D. Dissoint
11
271 ( P, Q ) and ( R ) are three sets and ( xi P cup Q cup )
( R . ) Given that ( n(xi)=60, n(P cap Q)=5 )
( n(Q cap R)=10, n(p)=20 ) and ( n(Q)=23 )
find ( nleft(P^{prime} cup Qright) )
A. 37
3. 38
( c cdot 45 )
D. 52
11
272 Thirty percent of the members of a swim club have passed the life saving test. Among the members who have not passed the test, 12 have taken
the preparatory course and 30 have not
taken the course.How many members
are there in the swim club?
A . 60
B. 80
( c .100 )
D. 120
E . 140
11
273 ( a, e ) is a subset of
( {x: x ) is a vowel in the English alphabet
( . text { Enter } 1 text { if true or } 0 text { otherwise }) )
11
274 If ( boldsymbol{A}={mathbf{1}, mathbf{4}, mathbf{9}, mathbf{1 6}, mathbf{2 5}, dots} ) and ( boldsymbol{B}= )
( left{boldsymbol{x} mid boldsymbol{x}=boldsymbol{n}^{2}, boldsymbol{n} in boldsymbol{N}right}, ) then
A ( . A=B )
в. ( A neq B )
c. ( A subset B )
D. ( B subset A )
11
275 Let ( boldsymbol{A}={mathbf{1}, mathbf{3}, mathbf{3}, mathbf{1}} ) and ( boldsymbol{B}={mathbf{1}, boldsymbol{4}} )
then:
( mathbf{A} cdot A neq B )
в. ( A=B )
( c cdot A subset B )
D. ( B subset A )
11
276 If ( X ) and ( Y ) are two sets then ( X cap(Y cup )
( X)^{prime} ) equals:
( mathbf{A} cdot X )
в. ( Y )
( c cdot phi )
D. {0}
11
277 ( boldsymbol{A} cap boldsymbol{X}=boldsymbol{B} cap boldsymbol{X}=boldsymbol{phi} & boldsymbol{A} cup boldsymbol{X}=boldsymbol{B} cup boldsymbol{X} )
prove that ( boldsymbol{A}=boldsymbol{B} )
11
278 If ( boldsymbol{A} subset boldsymbol{B}, ) then ( boldsymbol{A} cap boldsymbol{B} ) is
A. ( B )
в. ( A backslash B )
( c . A )
D. ( B backslash A )
11
279 In a class of 100 students, 55 students
have passed in physics and 67 students have passed in Mathematics. Find the number of students passed in Physics only.
11
280 Write down all possible subsets of the following set. {0,1} 11
281 ( operatorname{Let} U={1,2,3,4,5,6,7,8,9}, A= )
( {1,2,3,4}, B={2,4,6,8} ) and ( C= )
( {3,4,5,6} . ) Find (i) ( A^{prime}(text { ii }) B^{prime}(text { iii) }(A cup )
( C)^{prime}(text { iv })(A cup B)^{prime}(v)left(A^{prime}right)^{prime}left(text { vi) }(B-C)^{prime}right. )
11
282 Find union of ( A ) and ( B, ) and represent it
using Venn diagram:
( boldsymbol{A}={1,2,3,4,8,9}, B={1,2,3,5} )
11
283 The shaded region in the given figure is
( mathbf{A} cdot A cap(B cup C) )
в. ( A cup(B cap C) )
( mathbf{c} cdot A cap(B-C) )
D . ( A-(B cup C) )
11
284 The following table shows the percentage of the students of a school who participated in Election and Drawing competitions.

Competition Election Drawing
Percentage of Students
Draw a Venn diagram to represent this information and use it to find the
percentage of the students who
(i) Participated in Election only
(ii) Participated in Drawing only
(iii) Did not participate in any one of the competitions.

11
285 The total number of subsets of {1,2,6,7}
are?
A . 16
B. 8
c. 64
D. 32
11
286 ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} cup boldsymbol{B}) cap(boldsymbol{A} cup boldsymbol{C}) )
where ( boldsymbol{A}= )
( {1,2,4,5}, B{2,3,5,6}, C= )
{4,5,6,7} is ( A cup(B cap C)= )
( {1,2, a, b, 6} ) Find ( a+b )
11
287 ( {y: y ) is a point common to any two paral lel lines 3 is {y:yisapointcommontoanytwoparallel ines ( } ) a null set
A . True
B. False
11
288 Let ( A, B ) and ( C ) be the sets such that
( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cup boldsymbol{C} ) and ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} cap boldsymbol{C} )
Show that ( B=C )
11
289 If ( X ) and ( Y ) are two sets, then ( X cap )
( (boldsymbol{Y} cup boldsymbol{X})^{prime} ) equals
( mathbf{A} cdot X )
в. ( Y )
( c cdot phi )
D. None of these
11
290 If ( S ) is any set, then the family of all the
subsets of ( S ) is called the power set of ( S ) and it is denoted by ( P(S) . ) Power set of a
given set is always non-empty. If ( A ) has n elements, then ( P(A) ) has?
11
291 Draw the Venn diagram of ( boldsymbol{A} cap boldsymbol{B} ) 11
292 In a certain town, ( 25 % ) families own a
phone and ( 15 % ) own a car, ( 65 % ) families
own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard.
1) ( 10 % ) families own both a car and a
phone
Il) ( 35 % ) families own either a car or a
phone
III) 40,000 families live in the town.
Which of the above statements are
correct ?
A . ( I & I I )
в. I & III
c. II & III
D. I,II & III
11
293 Choose that set of numbers from the
option set that is similar to the given ( operatorname{set}{10,15,65} )
B . {124,5,3}
c. {95,25,5}
D. {168,15,4}
11
294 Write down all possible subsets of the following set.
( {a} )
11
295 ( boldsymbol{A}= )
( {x: x text { is a perfect square, } x<50, x in lambda )
( boldsymbol{B}= )
( {x: x=8 m+1, text { where } m in W, s<5 )
then find ( A cap B ) and display it with
Venn diagram.
11
296 Draw Venn diagrams to illustrate ( (boldsymbol{A} mid )
( boldsymbol{B}) cup(boldsymbol{A} backslash boldsymbol{C}) )
11
297 Which one of the following sets is
infinite?
A. Set of all integers greater than 5
B. Set ofall integers between ( -10^{10} ) and ( +10^{10} )
C. Set of all prime numbers between 0 and ( 10^{100} )
D. Set of all even prime numbers
11
298 Choose the correct answer from the
alternatives given :
From the details, find out the number of
rural people who are not educated
( A cdot 28 )
3. 16
( c cdot 44 )
25
11
299 State whether the following statement is true or false. Give reason to support
your answer.

A set can have infinitely many subsets.
A. True
B. False

11
300 While preparing the progress reports of the students, the class teacher found
that ( 70 % ) of the students passed in
Hindi, ( 80 % ) passed in English and only ( 65 % ) passed in both the subjects. Find
out the percentage of students who
failed in both the subjects.
A . ( 15 % )
B. 20%
c. ( 30 % )
D. ( 35 % )
11
301 ( P, Q ) and ( R ) are three sets and ( xi=P cup )
( Q cup R ) Given that ( n(xi)=60, n(P cap )
( Q)=5, n(Q cap R)=10, n(P)=20 ) and
( boldsymbol{n}(boldsymbol{Q})=23, ) find ( boldsymbol{n}(boldsymbol{P} cup boldsymbol{R}) )
A . 37
B . 38
c. 45
D. 52
11
302 Find ( A triangle B ) and draw Venn diagram when:
( A={a, b, c, d, e} ) and ( B={a, c, e, g} )
11
303 Find ( boldsymbol{n}left(boldsymbol{A} cap boldsymbol{C}^{c}right) ) 11
304 Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and
represent it by Venn diagram:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}}, boldsymbol{B}={boldsymbol{b}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} )
( mathbf{A} cdot{a, c, d, e} )
B ( cdot{d, e} )
( mathbf{c} cdot{a, b, c, d, e} )
D. None of these
11
305 Of the 200 students at College ( T ) majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from
A. 2020 to 50
B. 40 to 70
c. 50 to 130
D. 110 to 130
E. 110 to 150
11
306 If ( A ) and ( B ) be two finite sets such that
the total number of subsets of A is 960
more than the total number of subsets
of ( mathrm{B}, ) then ( n(A)-n(B) ) (where ( n(x) )
denotes the number of elements in set
( x ) ) is equal to?
11
307 Draw the appropriate Venn diagram for
( A^{prime} cap B^{prime} )
11
308 ( int frac{-sin x}{5+cos x} d x ) 11
309 If, ( A={5,7}, B={7,5}, ) then ( A ) and ( B )
are
A. Equal sets
B. Unequal sets
c. Null sets
D. None of these
11
310 ( A={x: x ) is a letter of the word ‘paper’
} and ( A=operatorname{set} ) of digists in the number
( mathbf{5 9 6 7 8} )
Sets ( A ) and ( B ) are equal
A. True
B. False
11
311 Decide whether sets ( A ) and ( B ) are equal
sets or not. ( boldsymbol{A}=mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, boldsymbol{B}={mathbf{x} mid mathbf{x} ) is a
positive even natural number less than
9
11
312 Use the Venn diagram to answer the
following questions
(i) List the elements of ( boldsymbol{U}, boldsymbol{E}, boldsymbol{F}, boldsymbol{E} cup boldsymbol{F} )
and ( boldsymbol{E} cap boldsymbol{F} )
(ii) Find ( n(U), n(E cup F) ) and ( n(E cap F) )
11
313 If ( A={1,2,3} B={4,5}, ) then find ( A-B )
( A cdot{1,4,5} )
B. {1,4,3}
( c cdot{1,2,3} )
( D cdot{4,5} )
11
314 ( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C}) )
( mathbf{A} cdot{1,6,7,8} )
в. {3,4,5}
( c cdot{2} )
( D . ) none
11
315 From the diagram, relation between ( A ) 11
316 The following is a example of empty set:
Set of all even natural numbers
divisible by 5
A . True
B. False
11
317 Find the equivalent set for ( boldsymbol{A}-boldsymbol{B} )
A ( . A cup(A cap B) )
B. B – A
c. ( A-(A cap B) )
D. ( A cap B )
11
318 In a class consisting of 100 students, 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi. The number of students knowing both Hindi and English is:
A. 5
B. 10
c. 15
D. 20
11
319 Which of the following sets are finite
sets.
(i) The sets of months in a year.
( (i i){1,2,3, dots} )
( (i i i){1,2,3, dots, 99,100} )
( (i v) ) The set of positive integers greater
than 100 .
A. ( ( i ) ) and ( (i i i) )
B. (i) only
c. ( (i i),(i i i) ) and ( (i v) )
D. (ii) and (iv)
11
320 Given, ( boldsymbol{A}={text { Quadrilaterals }}, boldsymbol{B}={ )
Rectangles ( }, C={text { Squares }}, D={ ) Rhombuses ( } . ) State whether the
following statement is correct or
incorrect. Give reasons.
( boldsymbol{D} subset boldsymbol{A} )
11
321 Find the following set is singleton set or
not.
( A={x: 7 x-3=11} )
11
322 f ( n(U)=50, n(A)=20, nleft((A cup B)^{prime}right)=18 )
then ( n(B-A) ) is
A . 14
B. 12
c. 16
D. 20
11
323 If ( boldsymbol{A}={1,2,3,4}, ) what is the number of
subsets of A with at least three
elements?
( mathbf{A} cdot mathbf{3} )
B. 4
( c .5 )
D. 10
11
324 Let ( Q ) be a non empty subset of ( N )
and ( q ) is a statement as given below:
( boldsymbol{q}: ) There exists an even number ( boldsymbol{a} in boldsymbol{Q} )
Negation of the statement ( boldsymbol{q} ) will be :
A. There is no even number in the set ( Q )
B. Every ( a in Q ) is an odd number
c. ( (a) ) and ( (b) ) both
D. None of these
11
325 Given ( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}, boldsymbol{h}} ) and ( boldsymbol{B}= )
( {a, e, i, o, u} )
then ( B-A ) is equal to
A ( cdot{i, o, u} )
в. ( {a, b, c} )
c. ( {c, d, e} )
D. ( {a,, i, z} )
11
326 00
0
00
0
11
327 If ( boldsymbol{f}={(boldsymbol{4}, boldsymbol{5}),(boldsymbol{5}, boldsymbol{6}),(boldsymbol{6},-boldsymbol{4})} ) and ( boldsymbol{g}= )
( {(boldsymbol{4},-boldsymbol{4}),(boldsymbol{6}, boldsymbol{5}),(boldsymbol{8}, boldsymbol{5})} . ) Then ( |boldsymbol{f}-boldsymbol{g}|=? )
11
328 set of irrational numbers is ( {sqrt{mathbf{8}}, boldsymbol{pi}} )
A . True
B. False
11
329 ( A-(A-B) ) is equivalent to which
expression
A. ( B )
в. ( A cup B )
c. ( A cap B )
D. ( B-A )
11
330 The set ( S:{1,2,3, ldots ., 12} ) is to be
partitioned into three sets ( A, B, C ) of equal size. Thus, ( boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}=boldsymbol{S}, boldsymbol{A} cap )
( boldsymbol{B}=boldsymbol{B} cap boldsymbol{C}=boldsymbol{A} cap boldsymbol{C}=boldsymbol{phi} . ) The number
of ways to partition ( S ) is
A ( cdot frac{12 !}{3 !(4 !)^{3}} )
в. ( frac{12 !}{3 !(3 !)^{4}} )
c. ( frac{12 !}{(4 ! !)^{3}} )
D. ( frac{12 !}{(3 !)^{4}} )
11
331 For any two sets ( A ) and ( B, A=B ) is
equivalent to
This question has multiple correct options
( mathbf{A} cdot A-B=B-A )
( mathbf{B} cdot A cup B=A cap B )
( mathbf{c} . A cup C=B cup C ) and ( A cap C=B cap C ) for any set ( C )
( mathbf{D} cdot A cap B=phi )
11
332 If ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1 0}) ) and
( boldsymbol{C}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq 7} ; ) find :
( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C}) )
11
333 Classify the following set as ‘singleton’
or ’empty’: ( B={y mid y ) is an odd prime
number ( <4} )
A. singleton
B. Empty
c. Data insufficient
D. None of these
11
334 {1,2,3}( nsubseteq{1,3,5} ) as ( m notin{1,3,5} )
Then ( m ) is:
11
335 Find the intersection of ( A ) and ( B ) by
representing using by Venn diagram:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}}, boldsymbol{B}={1,2, boldsymbol{9}} )
( A cdot phi )
в. ( a, b, c, 1,2,9 )
c. ( a, c, 1,9 )
D. None of these
11
336 The elements of ( (boldsymbol{A}-boldsymbol{B}) ) are: 11
337 The numbers shown in the Venn
diagram represent the number of
elements in each subset. Find ( [(boldsymbol{F} cup )
( boldsymbol{G}) cap boldsymbol{H}^{prime} )
( A cdot 3 )
B. 13
( c cdot 15 )
D. 18
11
338 State whether the following statement is true or false. Give reason to support
your answer.

For any two sets ( A ) and ( B ) either ( A subseteq B )
or ( boldsymbol{B} subseteq boldsymbol{A} )
A . True
B. False

11
339 In the given figure, how many people
study only 2 subjects?
Mathematics
A . 11
( B .23 )
( c cdot 12 )
D. 40
11
340 A marketing firm determined that, of
200 households surveyed, 80 used
neither Brand A nor Brand B soap, 60
used only Brand A soap, and for every household that used both brands of
soap, 3 used only Brand B soap. How
many of the 200 households surveyed used both brands of soap?
A . 15
B. 20
c. 30
D. 40
E . 45
11
341 Prove by using venn diagram
( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C})=(boldsymbol{A}-boldsymbol{B}) cap(boldsymbol{A}-boldsymbol{C}) )
11
342 State, whether the following pairs of
sets are equal or not:
If they are equal then write 1 , else write
( mathbf{0} )
( A=2,4,6,8 ) and ( B={2 n: n epsilon N ) and
( boldsymbol{n}<mathbf{5}} )
11
343 If ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi} ) and ( boldsymbol{B}-boldsymbol{A}=boldsymbol{phi} ) then ( mathbf{A} )
and B are
A. Overlapping
B. Equivalent
c. Dissiont
D. Equal
11
344 Every subset of an infinite set is
infinite.?
11
345 The relationship illustrated by the given
Venn diagram is :
( mathbf{A} cdot(A cup B) cap C )
( mathbf{B} cdot(A cap B) cap C )
( mathbf{c} cdot(A cap C) cup B )
( mathbf{D} cdot(A cup B)^{prime} cap C )
11
346 Find the total number of subsets of
each of the following set:
( boldsymbol{C}={boldsymbol{x} mid boldsymbol{x} in boldsymbol{W}, boldsymbol{x} leq 2} )
11
347 Set of concentric circle in a plane 11
348 ( boldsymbol{A}-[boldsymbol{B} cup boldsymbol{C} cup boldsymbol{D}]=(boldsymbol{A}-boldsymbol{B}) cap ldots ldots cap )
A ( . A-C ) and ( A-D )
B. ( C-A ) and ( A-D )
c. ( C-A ) and ( D-A )
D. ( A-C ) and ( D-A )
11
349 An investigator interviewed 100 students to determine their
preferences for the three drinks : milk (M), coffee (C) and tea
(1). He reported the following: 10 students had all the three
drinks M, C and T: 20 had M and C: 30 had C and T, 25 had
Mand T; 12 had M only: 5 had C only, and 8 had T only.
Using a Venn diagram find how many did not take any of
the three drinks.
(1978)
11
350 Suppose A1, A2, …….. A30 are thirty sets each with five
elements and B, B2, ……. B. are n sets each with thre
30 n .
elements. Let U A; = U B; = S. Assume that each
i= j=1
element of S belongs to exactly ten of the Ai’s and to exactly
11
351 If ( zeta ) is the set of boys in your school and
( B ) is the set of boys who play badminton Draw a Venn-diagram showing that
some of boys do not play badminton. If
( boldsymbol{n}(boldsymbol{zeta})=mathbf{4 0} ) and ( boldsymbol{n}left(boldsymbol{B}^{prime}right)=mathbf{1 7} ; ) find how
many play badminton.
11
352 The question is based on the Venn
Diagram. The circle stands for rural Triangle stands for educated, square
stands for hard-working and Rectangle stands for intelligent persons. The
number given represents a serial
number of the area

Which area represents ” Intelligent hard-working and educated but not
rural” persons?
( A cdot 12 )
в. 10
( c )
( D )

11
353 Which of the following sets is infinite?
A. ( {x: x text { is neither prime, nor composite }}, x in N )
B. The set of all rivers in India
C. Set of concentric circles
D. ( A={x: x text { is a letter of the English alphabet }} )
11
354 If ( boldsymbol{X}={1,2,3, dots, 10} ) and ( A= )
( {1,2,3,4,5} . ) Then, the number of
subsets ( B ) of ( X ) such that ( A-B={4} )
is
( A cdot 2^{5} )
B ( cdot 2^{4} )
( mathbf{c} cdot 2^{5}-1 )
D.
E ( .2^{4}-1 )
11
355 State true or false.
Given universal set= ( = ) ( left{-mathbf{6},-mathbf{5} frac{mathbf{3}}{mathbf{4}},-sqrt{mathbf{4}},-frac{mathbf{3}}{mathbf{5}},-frac{mathbf{3}}{mathbf{8}}, mathbf{0}, frac{mathbf{4}}{mathbf{5}}, mathbf{1}, mathbf{1} frac{mathbf{2}}{mathbf{3}}right. )
From the given set, find set of non-
negative integers is {0,1}
A. True
B. False
11
356 Find ( A triangle B ) and by definition:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}} ) and ( boldsymbol{B}={mathbf{1}, mathbf{3}, mathbf{5}, mathbf{7}} )
11
357 Let ( A, B ) and ( C ) be sets such that ( phi= )
( boldsymbol{A} cap boldsymbol{B} subseteq boldsymbol{C} . ) Then which of the following
statements is not true?
( mathbf{A} cdot ) If ( (A-C) subseteq B, ) then ( A subseteq B )
в. ( (C cup A) cap(C cup B)=C )
c. If ( (A-B) subseteq C ), then ( A subseteq C )
D. ( B cap C neq phi )
11
358 Define subset of a set. 11
359 Suppose ( U= )
( {3,4,5,6,7,8,9,10,11,12,13}, A= )
( {3,4,5,6,9}, B={3,7,9,5} ) and ( C= )
( {6,8,10,12,7} . ) Write down the
following set and draw Venn diagram
for:
( boldsymbol{A}^{prime} )
11
360 An investigator interviewed 100 students to determine their preferences for the three drinks: milk ( ( M ) ), coffee
( (C) ) and tea ( (T) . ) He reported the following: 10 students had all the three drinks ( M, C, T ; 20 ) had ( M ) and ( C ) only; ( mathbf{3 0} ) had ( boldsymbol{C} ) and ( boldsymbol{T} ; mathbf{1 2} ) had ( boldsymbol{M} ) only ( ; mathbf{5} ) had ( C ) only; 8 had ( T ) only. Then how many did not take any of three drinks is
A . 20
B. 30
( c .36 )
D. 42
11
361 If ( boldsymbol{A}={boldsymbol{m}, boldsymbol{a}, boldsymbol{t}, boldsymbol{h}, boldsymbol{e}, boldsymbol{m}, boldsymbol{a}, boldsymbol{t}, boldsymbol{i}, boldsymbol{c}, boldsymbol{s}}, boldsymbol{B}= )
( {a, m, t, h, e, i, c, s}, ) then:
A ( . A=B )
в. ( A neq B )
c. ( A subset B )
D. ( B subset A )
11
362 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{C} )
11
363 The set of all animals on the earth is a
A. Finite set
B. singleton set
c. Null set
D. Infinite set
11
364 000
0
0
( infty )
00
11
365 The set ( {x: x neq x} ) may be equal to
( A cdot{0} )
B. {1}
( c cdot{3} )
( D cdot{phi} )
11
366 If ( boldsymbol{A}-boldsymbol{B}=emptyset, ) then relation between ( mathbf{A} )
and B is :
( mathbf{A} cdot A neq B )
в. ( B subset A )
( c . A subset B )
D. ( A=B )
11
367 Draw Venn diagrams to illustrate ( boldsymbol{A} backslash boldsymbol{B} ) 11
368 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{D} )
11
369 The following is an example of empty
set:
( {x: x text { is a natural number, } xmathbf{1 2}} )
A. True
B. False
11
370 The shaded region in the Venn diagram
represents
11
371 The Venn diagram shows sets ( P, Q ) and ( R ) with regions labelled, I, II, III and IV.
State the region which represents set
( left[boldsymbol{P} cap(boldsymbol{Q} cup boldsymbol{R})^{prime}right] )
4
B.
( c )
( D cdot|v| )
11
372 In a group, if ( 60 % ) of people drink tea and ( 70 % ) drink coffee. What is the
maximum possible percentage of people drinking either tea or coffee but
not both?
( mathbf{A} cdot 100 % )
B. ( 70 % )
( c .30 % )
D. ( 10 % )
11
373 In the Venn diagram, the universal set, ( boldsymbol{xi}=boldsymbol{P} cup boldsymbol{Q} cup boldsymbol{R} )
Which of the four regions labelled ( A, B, C )
and D represents the sets ( boldsymbol{P} cap boldsymbol{Q} cap boldsymbol{R} ) ?
( A )
B
( c . c )
( D )
11
374 Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{D}-boldsymbol{A} )
11
375 If ( boldsymbol{B}=left{boldsymbol{y} mid boldsymbol{y}^{2}=boldsymbol{3} boldsymbol{6}right} ) then the ( operatorname{set} boldsymbol{B} ) is a
set.
A. Empty
B. singleton
c. Infinite
D. None of the above
11
376 The shaded region in the adjoining
diagram represents
A ( . A-B )
B. ( B-A )
( mathbf{c} cdot A Delta B )
D. ( A )
11
377 In a class of 50 students 35 opted for
Mathematics and 37 opted for Biology How may have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects)
A . 15
B. 17
c. 13
D. 19
11
378 In the Venn diagram, ( boldsymbol{xi}=boldsymbol{F} cup boldsymbol{G} cup boldsymbol{H} )
The shaded region in the diagram
represents set
( A cdot(F cap H)^{prime} cup G )
в. ( (F cup H) cap G )
c. ( G cup(F cap H) )
D. ( G cap(F cup H) )
11
379 Which of the following is equivalent set
(i) ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{5}, mathbf{7}} )
(ii) ( B={a, e, i, o, u} )
(iii) ( boldsymbol{C}={-mathbf{1},-mathbf{9},-mathbf{8},-mathbf{7}} )
A. (i) and (ii)
B. (i) and (iii)
c. (ii) and (iii)
D. None of these
11
380 If ( boldsymbol{A} cap boldsymbol{B} subseteq boldsymbol{C} ) and ( boldsymbol{A} cap boldsymbol{B} neq boldsymbol{phi} ). Then
which of the following is incorrect
( mathbf{A} cdot(A cup B) cap C neq phi )
в. ( B cap C=phi )
c. ( A cap C neq phi )
D. If ( (A-C) subseteq C ) then ( A subseteq C )
11
381 reflexive, symmetric and transitive.
This question has multiple correct options
( A cdot R_{3}={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)} )
( mathbf{B} cdot R_{3}= )
( {(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(4, )
( mathbf{c} cdot R_{3}={(1,1),(2,2),(3,3),(4,4)} )
D. none of these
11
382 If ( M={b, h, i} ; N={b, c, d, e} ) and
( boldsymbol{S}={boldsymbol{e}, boldsymbol{f}, boldsymbol{g}}, ) determine ( boldsymbol{M} cap boldsymbol{N} cap boldsymbol{S} )
and represent it in a Venn diagram.
11
383 Draw venn diagram ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C}) ) 11
384 From the given diagram find the number of elements in ( left(A^{prime} cup B^{prime}right) ) 11
385 Find total number of subsets of ( {p: p ) is a letter in the word ‘poor’? 11

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